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On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Convexity of Banach Spaces

On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Convexity of Banach Spaces

We show that every U ‐space and every Banach space X satisfying δ X (1) &gt; 0 are P (3)‐convex, and we study the nonuniform version of P ‐convexity, which we call p ‐convexity.